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arXiv · 2501.04370

Stability of constant equilibria in a Keller--Segel system with gradient dependent chemotactic sensitivity and sublinear signal production

Shohei Kohatsu
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Abstract

This paper deals with the homogeneous Neumann boundary-value problem for the Keller--Segel system \begin{align*} \begin{cases} u_t=Δu - χ\nabla \cdot (u|\nabla v|^{p-2}\nabla v),\\[] v_t=Δv - v + u^θ \end{cases} \end{align*} in $n$-dimensional bounded smooth domains for suitably regular nonnegative initial data, where $χ> 0$, $p \in (1, \infty)$ and $θ\in (0,1]$. Under smallness conditions on $p$ and $θ$, we prove that the spatially homogeneous equilibrium solution is stable. This generalizes the result in Kohatsu--Yokota (Le Matematiche, 2023; 78; 213--237) from the case $θ= 1$ to more general values of $θ$.

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Shohei Kohatsu. 2025-01-08. Stability of constant equilibria in a Keller--Segel system with gradient dependent chemotactic sensitivity and sublinear signal production. https://arxiv.org/abs/2501.04370

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